MathDB

Dragos, the early ruler of Moldavia, and Maria the Oracle play the following game. Firstly, Maria chooses a set

S

of prime numbers. Then Dragos gives an infinite sequence

x_1, x_2, ...

of distinct positive integers. Then Maria picks a positive integer

M

and a prime number

p

from her set

S

. Finally, Dragos picks a positive integer

N

and the game ends. Dragos wins if and only if for all integers

n \ge N

the number

x_n

is divisible by

p^M

; otherwise, Maria wins. Who has a winning strategy if the set S must be:

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a) finite;

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b) infinite?
Proposed by Boris Stanković, Bosnia and Herzegovina

N4